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\newtheorem{theorem}{Theorem}
\newtheorem{acknowledgement}[theorem]{Acknowledgement}
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\newtheorem{axiom}[theorem]{Axiom}
\newtheorem{case}[theorem]{Case}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{conclusion}[theorem]{Conclusion}
\newtheorem{condition}[theorem]{Condition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{criterion}[theorem]{Criterion}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{exercise}[theorem]{Exercise}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{problem}[theorem]{Problem}
\newtheorem{proposition}[theorem]{Proposition}
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\begin{document}
Si $\ f(x)=\dfrac{x+1}{x-1}$ entonces $f(f(a))$ es:\newline\qquad a) $a\qquad
$b) $\dfrac{a-1}{a+1}\qquad$c) $\dfrac{1}{a}\qquad$d)\textbf{\ }$\dfrac
{a+1}{a-1}$

Si $\ f(x)=\dfrac{x-1}{x+1}$ entonces $f(f(a))$ es:\newline\qquad a)
$\dfrac{1}{a}\qquad$b) $\dfrac{a-1}{a+1}\qquad$c) $a\qquad$d)\textbf{\ }%
$\dfrac{a+1}{a-1}$

Si $\ f(x)=\dfrac{2x+2}{2x-2}$ entonces $f(f(a))$ es:\newline\qquad a)
$2a\qquad$b) $2\left(  \dfrac{a-1}{a+1}\right)  \qquad$c) $\dfrac{2}{a}\qquad
$d)\textbf{\ }$2\left(  \dfrac{a+1}{a-1}\right)  $

Si $\ f(x)=\dfrac{2x+1}{3x-1}$ entonces $f(f(a))$ es:\newline\qquad a)
$\left(  7a+1\right)  \left(  3a+4\right)  \qquad$b) $\dfrac{2a+1}{3a-1}%
\qquad$c) $5a+1\qquad$d)\textbf{\ }$\left(  5a+1\right)  \left(  3a+4\right)
$

Si $\ f(x)=\dfrac{3}{x-1}$ entonces $f(f(a))$ es:\newline\qquad a)
$\dfrac{3a-3}{4-a}\qquad$b) $\dfrac{3}{a-1}\qquad$c) $\dfrac{4-a}{3a-3}\qquad
$d)\textbf{\ }$\dfrac{a}{a-1}$

Si $\ f(x)=\dfrac{x+5}{x-5}$entonces $f(f(a))$ es: \newline\qquad a)
\textbf{\ }$\mathbf{-}\dfrac{3a-10}{2a-15}$\qquad b) $a$\qquad c)
$-\dfrac{2a-5}{a+5}$\qquad d) $\dfrac{5}{a}$\qquad

Si $\ f(x)=\dfrac{x-3}{x+2}$ entonces $f(f(a))$ es: \newline\qquad a)
\textbf{\ }$-\dfrac{2a+9}{3a+1}$\qquad b) $\dfrac{2a-9}{3a-1}$\qquad c)
$\dfrac{3a+9}{2a+1}$\qquad d) $\dfrac{3a-9}{2a-1}$\qquad

Si $\ f(x)=\dfrac{x-9}{x+3}$ entonces $f(f(a))$ es: \newline\qquad a)
\textbf{\ }$-\dfrac{1}{a}(2a+9)$\qquad b) $a-3$\qquad c) $\dfrac{a-3}{a+3}%
$\qquad d) $\dfrac{a+9}{a-3}$\qquad

Si $\ f(x)=\dfrac{x-2}{x-5}$ entonces $f(f(a))$ es: \newline\qquad a)
\textbf{\ }$\dfrac{a-8}{4a-23}$\qquad b) $\dfrac{a-3}{a+5}$\qquad c)
$\dfrac{a-2}{a-5}$\qquad d) $\dfrac{a-7}{3a+23}$\qquad

Si $\ f(x)=\dfrac{x-4}{x+3}$ entonces $f(f(a))$ es: \newline\qquad a)
\textbf{\ }$-\dfrac{3a+16}{4a+5}$\qquad b) $\dfrac{3a+16}{4a-5}$\qquad c)
$\dfrac{3a-16}{4a-5}$\qquad d) $\dfrac{3a-16}{4a+5}$\qquad

Si $\ f(x)=\dfrac{x+5}{x-3}$ entonces $f(f(a))$ es: \newline\qquad a)
\textbf{\ }$-\dfrac{3a-5}{a-7}$\qquad b) $\dfrac{3a-5}{a+7}$\qquad c)
$\dfrac{3a+5}{a+7}$\qquad d) $\dfrac{3a-5}{a-7}$\qquad

Si $\ f(x)=\dfrac{x+2}{x-2}$ entonces $f(f(a))$ es: \newline\qquad a)
\textbf{\ }$-\dfrac{3a-2}{a-6}$\qquad b) $\dfrac{a+2}{a-2}$\qquad c)
$\dfrac{3a-2}{a-6}$\qquad d) $\dfrac{3a+2}{a+6}$

Si $\ f(x)=\dfrac{x+4}{x-4}$ entonces $f(f(a))$ es: \newline\qquad a)
\textbf{\ }$-\dfrac{5a-12}{3a-20}$\qquad b) $\dfrac{a+4}{a-4}$\qquad c)
$\dfrac{5a-12}{3a-20}$\qquad d) $\dfrac{5a+12}{3a+20}$\qquad

Si $\ f(x)=\dfrac{x-1}{x+3}$ entonces $f(f(a))$ es: \newline\qquad a)
\textbf{\ }$\mathbf{-}\dfrac{1}{a+2}$\qquad b) $\dfrac{1}{a+2}$\qquad c)
$\dfrac{a-1}{a+3}$\qquad d) $\dfrac{1}{a+3}$\qquad

Si $\ f(x)=\dfrac{x+1}{x+4}$ entonces $f(f(a))$ es: \newline\qquad a)
\textbf{\ }$\dfrac{2a+5}{5a+17}$\qquad b) $\dfrac{a+1}{a+4}$\qquad c)
$\dfrac{5a+5}{2a+17}$\qquad d) $\dfrac{2a+17}{5a+5}$\qquad


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